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Question:

If the coefficients of x³ and x⁴ in the expansion of (1+ax+bx²)(1-x)¹⁸ in powers of x are both zero, then (a,b) is equal to:

(16,2513)

(14,2513)

(14,2723)

(16,2723)

Solution:

1(1𕒶x)18+ax(1𕒶x)18+bx2(1𕒶x)18